Evolution of complexity following a quantum quench in free field theory

TL;DR

This paper investigates how circuit complexity evolves over time after a smooth mass quench in a free scalar field theory, revealing two phases of linear growth and saturation with oscillations, and showing dependence on the quench direction.

Contribution

It applies a recent circuit complexity proposal to analyze time evolution after a mass quench in free field theory, highlighting unique growth and saturation behaviors.

Findings

Complexity exhibits two phases: linear growth and saturation with oscillations.

Saturation time scale is proportional to the quench duration $\, ext{delta t}$.

Complexity can increase or decrease depending on whether the mass is increased or decreased.

Abstract

Using a recent proposal of circuit complexity in quantum field theories introduced by Jefferson and Myers, we compute the time evolution of the complexity following a smooth mass quench characterized by a time scale $\delta t$ in a free scalar field theory. We show that the dynamics has two distinct phases, namely an early regime of approximately linear evolution followed by a saturation phase characterized by oscillations around a mean value. The behavior is similar to previous conjectures for the complexity growth in chaotic and holographic systems, although here we have found that the complexity may grow or decrease depending on whether the quench increases or decreases the mass, and also that the time scale for saturation of the complexity is of order $\delta t$ (not parametrically larger).